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Chapter 11: Problem 98

A substance in which the valence and conduction bands overlap is (a) a semiconductor; (b) a metalloid; (c) a metal; (d) an insulator.

Short Answer

Expert verified
The correct answer is (c) a metal.

Step by step solution

01

Understand the Electronic Band Structure

In solid-state physics, the electronic band structure of a solid describes the range of energies that an electron within the solid may have (called energy bands, allowed bands, or simply bands) and ranges of energy that it may not have (called band gaps or forbidden bands). The term 'band' originates from the characteristic energy band structure that arises from the behavior of electrons in solids as a consequence of the indistinguishable nature of particles. The band structure of a solid determines its properties as an insulator, metal, or semiconductor.
02

Distinguish Between the Different Materials

Semiconductors, metalloids, and insulators have a band gap between the valence band and the conduction band. In metals, however, the valence and conduction bands overlap, allowing free movement of electrons. Therefore, metals can conduct electricity.
03

Answer the Question

Based on the above distinction, it is clear that the substance in which the valence and conduction bands overlap is a metal.

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Most popular questions from this chapter

Explain why the molecular structure of \(\mathrm{BF}_{3}\) cannot be adequately described through overlaps involving pure \(s\) and \(p\) orbitals.

Furan, \(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O},\) is a substance derivable from oat hulls, corn cobs, and other cellulosic waste. It is a starting material for the synthesis of other chemicals used as pharmaceuticals and herbicides. The furan molecule is planar and the \(\mathrm{C}\) and \(\mathrm{O}\) atoms are bonded into a fivemembered pentagonal ring. The H atoms are attached to the C atoms. The chemical behavior of the molecule suggests that it is a resonance hybrid of several contributing structures. These structures show that the double bond character is associated with the entire ring in the form of a \(\pi\) electron cloud. (a) Draw Lewis structures for the several contributing structures to the resonance hybrid mentioned above. (b) Draw orbital diagrams to show the orbitals that are involved in the \(\sigma\) and \(\pi\) bonding in furan. [Hint: You need use only one of the contributing structures, such as the one with no formal charges.] (c) How many \(\pi\) electrons are there in the furan molecule? Show that this number of \(\pi\) electrons is the same, regardless of the contributing structure you use for this assessment.

Describe the bond order of diatomic carbon, \(\mathrm{C}_{2},\) with Lewis theory and molecular orbital theory, and explain why the results are different.

Construct the molecular orbital diagram for CaF. Would you expect the bond length of \(\mathrm{CaF}^{+}\) to be longer or shorter than that of CaF?

Of the following, the species with a bond order of 1 is (a) \(\mathrm{H}_{2}^{+} ;\) (b) \(\mathrm{Li}_{2} ;\) (c) \(\mathrm{He}_{2} ;\) (d) \(\mathrm{H}_{2}^{-}\)
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